In testing the difference between two population means using two independent samples,we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference if:
A)the sample sizes are both large.
B)the populations are normal with equal variances.
C)the populations are non-normal with unequal variances.
D)All of these choices are true.

Question

In testing the difference between two population means using two independent samples,we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference  if:
A)the sample sizes are both large. 
B)the populations are normal with equal variances. 
C)the populations are non-normal with unequal variances. 
D)All of these choices are true.

Quizplus · Accepted Answer

In testing the difference between two population means using two independent samples, we use the pooled variance in estimating the standard error of the sampling distribution of the sample mean difference when the populations are normal with equal variances. The pooled variance combines the variances from both samples into one estimate, assuming that the population variances are equal. This results in a more accurate estimate of the standard error of the sampling distribution and improves the power of the hypothesis test. If the sample sizes are both large, a normal approximation can be used even if the populations are not normal or have unequal variances. However, in this case, the pooled variance may not be the best estimate of the true variance, and other methods may be more appropriate. Therefore, choice B is the best choice.

In Testing the Difference Between Two Population Means Using Two